Chapter 42 - Nuclear Physics - Problems - Page 1303: 17

$m_{\mathrm{n}} = 1.0086637$

As in many computations in this chapter, this circumstance (of implicitly including electron masses in what should be a purely nuclear calculation) does not cause extra difficulty in the calculation. Setting the gamma ray energy equal to $\Delta E_{\mathrm{be}},$ we solve for the neutron mass (with each term understood to be in u units): \begin{aligned} m_{\mathrm{n}} &=M_{\mathrm{d}}-m_{\mathrm{H}}+\frac{E_{\gamma}}{c^{2}}=2.013553212-1.007276467+\frac{2.2233}{931.502} \\ &=1.0062769+0.0023868\\ &= \boxed{1.0086637} \end{aligned}